The rheological properties of normal erythrocytes appear to be determined largely by those of the red cell membrane. In sickle-cell disease, the intracellular polymerization of sickle hemoglobin upon deoxygenation leads to a marked increase in intracellular viscosity and elastic stiffness, and also has indirect effects on the cell membrane. In order to estimate the components of abnormal cell rheology due to the polymerization process (and that due to the membrane abnormalities), we have developed a mathematical model of whole-cell deformability in narrow vessels. This model uses hydrodynamic lubrication theory to describe the pulsatile flow in the gap between a cell and the vessel wall. We use published values of normal and sickle cell membrane elastic moduli and of sickle hemoglobin viscous and elastic moduli as a function of oxygen saturation to estimate the cell deformation and relative hydrodynamic resistance as a function of oxygen saturation for sickle erythrocytes. The model should be useful for reconciling the vast and disparate sets of data available on the abnormal properties of sickle cell hemoglobin and sickle erythrocyte membranes--the two main factors that lead to pathology in patients with this disease. We are also developing models to study red cell heterogeneity with regard to intracellular hemoglobin concentration, as well as a large deformation membrane theory that includes bending and stretching.